Extending the Lax type operator for finite W-algebras

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• Jonathan Brown (SUNY Oneonta)
• Wednesday 19 April 2023, 15:00-16:00
• Lecture Theatre C, Watson Building.

If you have a question about this talk, please contact Matthew Westaway.

Finite W-algebras are intimately related to the geometry of nilpotent orbits and the infinite dimensional representation theory of Lie algebras. They are defined in terms of a nilpotent orbit, and they are an invariant subalgebra of a left ideal in universal enveloping algebra of a reductive Lie algebra. Outside of type A there is no known formula for calculating generators of these algebras (apart from specific examples). Recent work by Kac, De Sole, and Valeri has resulted in a Lax type operator which produces generators of an important subalgebra of a finite W-algebra, and in talk I will explain how their results can be extended. This results in a formula for generators of important classes of classical f finite W-algebras.

This talk is part of the Algebra seminar series.

This talk is included in these lists:

• Algebra seminar
• Lecture Theatre C, Watson Building
• School of Mathematics events

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